1. Accreting isolated neutron stars

2. Magnetic rotator
Observational appearances of NSs (if we are not speaking about cooling) are mainly determined by P, Pdot, V, B, (also, probably by the inclination angle β), and properties of the surrounding medium.
B is not evolving significantly in most cases, so it is important to discuss spin evolution.
Together with changes in B (and β) one can speak about magneto-rotational evolution
We are going to discuss the main stages of this evolution, namely:
Ejector, Propeller, Accretor, and Georotator following the classification by Lipunov

3. Evolution of neutron stars: rotation + magnetic field
Ejector → Propeller → Accretor → Georotator
1 – spin down
2 – passage through a molecular cloud
3 – magnetic field decay
[astro-ph/ ]
Mdot/μ2
See the book by Lipunov (1987, 1992)

4. Accreting isolated neutron stars
Why are they so important?
Can show us how old NSs look like
Magnetic field decay
Spin evolution
Physics of accretion at low rates
NS velocity distribution
New probe of NS surface and interiors
ISM probe

5. Critical periods for isolated NSs
Transition from Ejector to Propeller (supersonic)
Duration of the ejector stage
Transition from supersonic Propeller to subsonic Propeller or Accretor
A kind of equilibrium period for the case of accretion from turbulent medium
Condition for the Georotator formation (instead of Propeller or Accretor)
(see, for example, astro-ph/ )

6. Accretion dynamics Bondi-Hoyle-Littleton accretion (astro-ph/0406166)
Recently BHL accretion for non-magnetized accretors have been studied in
Still, resolution in 3D is not high enough.

7. Expected properties Accretion rate
An upper limit can be given by the Bondi formula:
Mdot = π RG2 ρ v, RG ~ v-2
Mdot = g/s (v/10 km/s) -3 n
L=0.1 Mdot c2 ~ 1031 erg/s
However, accretion can be smaller due to the influence of a magnetosphere of a NS (see numerical studies by Toropina et al ).
Periods
Periods of old accreting NSs are uncertain, because we do not know evolution
well enough.
RA=Rco

8. Reduction of the accretion rate

9. Subsonic propeller Even after Rco>RA accretion can be inhibited.
This have been noted already in the pioneer papers by Davies et al.
Due to rapid (however, subsonic) rotation a hot envelope is formed around the magnetosphere. So, a new critical period appear.
(Ikhsanov astro-ph/ )
If this stage is realized (inefficient cooling) then
accretion starts later
accretors have longer periods

10. Equilibrium period
Interstellar medium is turbulized. If we put a non-rotating NS in the ISM, then because of accretions of turbulized matter it’ll start to rotate. This clearly illustrates, that a spinning-down accreting isolated NS in a realistic ISM should reach some equilibrium period. RG
n=1 cm-3
n=0.1 cm-3
v<60
v<35
v<15 km s-1
[A&A 381, 1000 (2002)]
A kind of equilibrium period for the case of accretion from turbulent medium

11. Expected properties-2 3. Temperatures
Depend on the magnetic field. The size of polar caps depends on the field and accretion rate: ~ R (R/RA)1/2
4. Magnetic fields
Very uncertain, as models of the field decay cannot give any solid predictions for very long time scales (billions of years).
5. Flux variability.
Due to fluctuations of matter density and turbulent velocity in the ISM it is expected that isolated accretors are variable on a time scale
~ RG/v ~ days - months
Still, isolated accretors are expected to be numerous at low fluxes (their total number in the Galaxy is large than the number of coolers of comparable luminosity). They should be hotter than coolers, and have much longer spin periods.

12. Properties of accretors
In the framework of a simplified model (no subsonic propeller, no field decay, no accretion inhibition, etc.) one can estimate
properties of isolated accretors.
Slow, hot, dim, numerous at low fluxes (<10-13 erg/cm2/s)
Reality is more uncertain.
(astro-ph/ )

13. Accreting isolated NSs
At small fluxes <10-13 erg/s/cm2 accretors can become more abundant
than coolers. Accretors are expected to be slightly harder:
eV vs eV. Good targets for eROSITA!
From several hundreds up to
several thousands objects
at fluxes about few ∙10-14,
but difficult to identify.
Monitoring is important.
Also isolated accretors can
be found in the Galactic center
(Zane et al. 1996,
Deegan, Nayakshin 2006).
astro-ph/

14. Where and how to look for
As sources are dim even in X-rays, and probably are extremely dim in other bands it is very difficult to find them.
In an optimistic scenario they outnumber cooling NSs at low fluxes.
Probably, for ROSAT they are to dim.
We hope that eROSITA will be able to identify accreting INSs.
Their spatial density at fluxes ~10-15 erg/cm2/s is expected to be ~few per sq.degree in directions close to the galactic plane.
It is necessary to have an X-ray survey at ~ eV with good resolution.
In a recent paper by Muno et al.the authors put interesting limits on the number of unidentified magnetars. The same results can be rescaled to give limits on the M7-like sources.

15. “Decayed” field distribution
We assume the field to be constant, but as an initial we use the “decayed” distribution, following Popov et al
Boldin, Popov 2010

16. Simple semianalytical model
Fraction of accretors for different magnetic fields and ISM density. Kick velocity distribution is taken following Arzoumanian et al. (2002).
With subsonic
Without subsonic
Boldin, Popov 2010

17. Individual tracks Individual tracks in the semianalytical model.
Clearly, even with long subsonic propeller stage highly magnetized NSs (like the M7) can become accretors relatively soon.
Boldin, Popov 2010

18. Final distributions
Filled symbols – “decayed distribution”. Open squares – delta-function μ30=1.
Accretors
Propellers
Subsonic Propellers
Ejectors
Georotators
Boldin, Popov 2010

19. Who forms accretors?
NSs with stronger fields form more accretors, unless their field and velocities are so high, that they become Georotators.
Boldin, Popov 2010

20. Running out of the Galaxy
2/3 of NSs leave the Galaxy. Mostly, they stay as Ejectors, or become Georotators.
In the solar vicinity fractions of INSs at different evolutionary stages are: - Ejectors: % - Propellers: negligible
- subsonic P.: % - Accretors: % Georotators: negligible
Boldin, Popov 2010

21. Some conclusions
Highly magnetized INS (as the M7) can become Accretors even taking into account long subsonic Propeller stage.
In the solar vicinity fractions of INSs at different evolutionary stages are: - Ejectors: % - Propellers: negligible
- subsonic P.: % - Accretors: % Georotators: negligible
Boldin, Popov 2010

22. Settling accretion onto INSs
At low X-ray luminosities the captured matter, heated in the bow-shock, has no time to cool down and remains hot, which prevents it from entering the NS magnetosphere via Rayleigh-Taylor (RT) instability.
Thus, steady accretion luminosity is expected to be low, however, flares with duration hours-day are possible. Maximum luminosity can be ~1031 erg/s.

23. Papers to read Treves et al. PASP 112, 297 (2000)
Popov et al. ApJ 530, 896 (2000)
Popov, Prokhorov Physics Uspekhi 50, 1123 (2007) Ch. 5.4
Boldin, Popov MNRAS  vol. 407, pp (2010)
Edgar astro-ph/
Popov et al. MNRAS 487, 2817 (2015)